منابع مشابه
Eulerian polynomials
A short report on my lecture at the Conference in Honor of W. Killing in Münster on December 7, 2007, together with some remarks on the preceding paper by ArjehM. Cohen. I reported on Euler’s famous paper Remarques sur un beau rapport entre les series des puissances tant direct que reciproques, Académie des sciences de Berlin, Lu en 1749, Opera Omnia Serie I, Bd. 15, pp. 70-90. In modern termin...
متن کاملThe (1/k)-Eulerian Polynomials
We use the theory of lecture hall partitions to de ne a generalization of the Eulerian polynomials, for each positive integer k. We show that these 1=k-Eulerian polynomials have a simple combinatorial interpretation in terms of a single statistic on generalized inversion sequences. The theory provides a geometric realization of the polynomials as the h -polynomials of k-lecture hall polytopes. ...
متن کاملEulerian polynomials of spherical type
The Eulerian polynomial of a finite Coxeter system (W, S) of rank n records, for each k ∈ {1, . . . , n}, the number of elements w ∈ W with an ascent set {s ∈ S | l(ws) > l(w)} of size k, where l(w) denotes the length of w with respect to S. The classical Eulerian polynomial occurs when the Coxeter group has type An, so W is the symmetric group on n + 1 letters. Victor Reiner gave a formula for...
متن کاملLaurent polynomials and Eulerian numbers
Article history: Received 24 August 2009 Available online 25 February 2010
متن کاملEulerian polynomials and B-splines
Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, Bsplines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann zeta function values at odd integers are given. The relation between Eulerian numbers a...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1991
ISSN: 0002-9947
DOI: 10.2307/2001806